Explanation Given information: Diameter of the shaft is 100 mm. Shaft rotates at 500 rpm. Turbine develops 150 kW of power. Gear C and gear D receives equal amount of power. Calculation: The expression for angular velocity of the shaft ( ω ) is shown below: ω = 2 π f Here, the frequency of shaft’s rotation is f . Substitute 500 rev min for f . ω = 2 π ( 500 rev min ) = 2 π ( 500 rev min × 1 min 60 sec ) = 52.36 rad sec The expression for the power transmitted ( P ) by the shaft is shown below: P = T ω Here, the applied torque is T and the angular velocity of the shaft is ω . Rearrange Equation to find the torque. T = P ω Substitute 150 kW for P and 52.36 rad sec for ω . T = 150 kW 52.36 rad sec = 150 kW ( 10 3 W 1 kW ) 52.36 rad sec = 2 , 864.789 N ⋅ m Find the torque at C and D . Gear C and Gear D receives equal amount of power. T C = T D = T 2 = 1 , 432.394 Sketch the internal torque T shown in Figure 1. Sketch the internal torque at gear C and gear D of the shaft as shown in Figure 2. Refer Figure 1 and Figure 2. The maximum value of torque occurs in the region BC of the shaft with the value of 2,864.789 N.m. The radius of the shaft is r with the value of 50 mm. The polar moment of inertia for a solid shaft of radius ( r ) is π 2 r 4 . The torsion formula for maximum shear stress in the solid shaft ( τ max ) is shown below: τ max = T C c J Here, the maximum torque in the segment BC is T C , the polar moment of inertia is J , and the outer radius of the shaft is c . Substitute r for c and π 2 r 4 for J . τ max = T C r π 2 r 4 = 2 T C π r 3 Substitute 2 , 864.789 N ⋅ m for T C and 50 mm for r . τ max = 2 ( 2 , 864.789 N ⋅ m ) π ( 50 mm ) 3 = 2 ( 2 , 864.789 N ⋅ m × 10 3 mm 1 m ) π ( 50 mm ) 3 = 14.6 MPa Therefore, the absolute maximum shear stress in the shaft is 14.6 MPa _ . Refer Figure 2. The value of torque T B C is 2 , 864.789 N ⋅ m , T C D is 1 , 432.394 N ⋅ m , and T D E is 0

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Design of Shafts and Shaft Components

The shaft is basically defined as the machine element that rotates, is in circular cross-section, it is majorly used to transfer the power from one part of the system to another, or from a power generating machine to a power absorbing machine. The shaft …

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Chapter 10.4, Problem 46P

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Find the absolute maximum shear stress in the shaft and the angle of twist of end B of the shaft relative to E.

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Chapter 10.4, Problem 45P

Chapter 10.4, Problem 47P

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Chapter 10 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 10.3 - Determine the internal torque at each section and...Ch. 10.3 - Determine the internal torque at each section and...Ch. 10.3 - Prob. 3PP Ch. 10.3 - Prob. 4PP Ch. 10.3 - Prob. 1FP Ch. 10.3 - The hollow circular shaft is subjected to an...Ch. 10.3 - Prob. 3FP Ch. 10.3 - Prob. 4FP Ch. 10.3 - Determine the maximum shear stress in the shaft at...Ch. 10.3 - Prob. 6FP

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Find the absolute maximum shear stress in the shaft and the angle of twist of end B of the shaft relative to E .

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Find the absolute maximum shear stress in the shaft and the angle of twist of end B of the shaft relative to E.

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Chapter 10 Solutions